library(tidyverse) # data manipulation
library(ggpubr) # producing data exploratory plots
library(modelsummary) # descriptive data
library(glmmTMB) # running generalised mixed models
library(DHARMa) # model diagnostics
library(performance) # model diagnostics
library(ggeffects) # partial effect plots
library(car) # running Anova on model
library(emmeans) # post-hoc analysis m1 <- read_csv("import_data/1_month_size_data_2022_2023.csv") |>
mutate(across(1:15,factor)) |>
mutate(STANDARD_LENGTH =LENGTH,
.keep = "unused") |>
select(!(NOTES)) |>
select(1:15,"STANDARD_LENGTH","MASS") |>
group_by(CLUTCH_NUMBER) |>
mutate(DENSITY = n()) |>
ungroup()
m2 <- read_csv("import_data/2_month_size_data_2022_2023.csv") |>
mutate(across(1:15,factor)) |>
mutate(STANDARD_LENGTH=LENGTH,
.keep = "unused") |>
select(!(NOTES)) |>
select(1:15,"STANDARD_LENGTH","MASS")|>
group_by(CLUTCH_NUMBER) |>
mutate(DENSITY = n()) |>
ungroup()
m2.5 <- read_csv("import_data/2-5_month_size_data_2022_2023.csv") |>
mutate(across(1:15,factor)) |>
mutate(STANDARD_LENGTH =LENGTH,
.keep = "unused") |>
select(!(NOTES)) |>
select(1:15,"STANDARD_LENGTH","MASS")|>
group_by(CLUTCH_NUMBER) |>
mutate(DENSITY = n()) |>
ungroup()
adult <- read_csv("import_data/adult_size_2022_2023.csv") |>
mutate(across(1:3,factor),
MALE = FISH_ID,
FEMALE = FISH_ID,
POPULATION = str_sub(FISH_ID, 2,4),
POPULATION = case_when(POPULATION == "ARL" ~ "Arlington Reef",
POPULATION == "SUD" ~ "Sudbury Reef",
POPULATION == "VLA" ~ "Vlassof cay",
POPULATION == "PRE" ~ "Pretty patches",
TRUE ~ POPULATION)) |>
left_join(select(m1, c("MALE","TEMPERATURE")),
by="MALE") |>
left_join(select(m1, c("FEMALE","TEMPERATURE")),
by="FEMALE") |>
distinct() |>
mutate(TEMPERATURE = coalesce(TEMPERATURE.x, TEMPERATURE.y)) |>
drop_na(TEMPERATURE) |>
select(-c("TEMPERATURE.x","TEMPERATURE.y"))m1_df <- m1 |>
left_join(select(adult, c("MALE", "SL", "MASS")),
by ="MALE") |>
mutate(SL_MALE =SL,
MASS_MALE =MASS.y,
.keep = "unused") |>
left_join(select(adult, c("FEMALE", "SL", "MASS")),
by ="FEMALE") |>
mutate(SL_FEMALE =SL,
MASS_FEMALE =MASS,
.keep ="unused") |>
mutate(SL_MIDPOINT = (SL_MALE+SL_FEMALE)/2,
MASS_MIDPOINT = (MASS_MALE+MASS_FEMALE)/2) |>
group_by(CLUTCH_NUMBER) |>
mutate(MEDIAN_MASS = median(MASS.x)) |>
drop_na(MEDIAN_MASS) |>
ungroup() |>
select(-c("STANDARD_LENGTH","MASS.x", "SAMPLE_NO")) |>
distinct() |>
mutate(MASS_MIDPOINT =coalesce(MASS_MIDPOINT, MASS_MALE),
SL_MIDPOINT =coalesce(SL_MIDPOINT, SL_MALE))
m2_df <- m2 |>
left_join(select(adult, c("MALE", "SL", "MASS")),
by ="MALE") |>
mutate(SL_MALE =SL,
MASS_MALE =MASS.y,
.keep = "unused") |>
left_join(select(adult, c("FEMALE", "SL", "MASS")),
by ="FEMALE") |>
mutate(SL_FEMALE =SL,
MASS_FEMALE =MASS,
.keep ="unused") |>
mutate(SL_MIDPOINT = (SL_MALE+SL_FEMALE)/2,
MASS_MIDPOINT = (MASS_MALE+MASS_FEMALE)/2) |>
group_by(CLUTCH_NUMBER) |>
mutate(MEDIAN_MASS = median(MASS.x)) |>
drop_na(MEDIAN_MASS) |>
ungroup() |>
select(-c("STANDARD_LENGTH","MASS.x", "SAMPLE_NO")) |>
distinct() |>
mutate(MASS_MIDPOINT =coalesce(MASS_MIDPOINT, MASS_MALE),
SL_MIDPOINT =coalesce(SL_MIDPOINT, SL_MALE))
m2.5_df <- m2.5 |>
left_join(select(adult, c("MALE", "SL", "MASS")),
by ="MALE") |>
mutate(SL_MALE =SL,
MASS_MALE =MASS.y,
.keep = "unused") |>
left_join(select(adult, c("FEMALE", "SL", "MASS")),
by ="FEMALE") |>
mutate(SL_FEMALE =SL,
MASS_FEMALE =MASS,
.keep ="unused") |>
mutate(SL_MIDPOINT = (SL_MALE+SL_FEMALE)/2,
MASS_MIDPOINT = (MASS_MALE+MASS_FEMALE)/2) |>
group_by(CLUTCH_NUMBER) |>
mutate(MEDIAN_MASS = median(MASS.x)) |>
drop_na(MEDIAN_MASS) |>
ungroup() |>
select(-c("STANDARD_LENGTH","MASS.x")) |>
distinct() |>
mutate(MASS_MIDPOINT =coalesce(MASS_MIDPOINT, MASS_MALE),
SL_MIDPOINT =coalesce(SL_MIDPOINT, SL_MALE))|>
drop_na(MASS_MALE)plot1 <- ggplot(m1_df, aes(x=MASS_MALE, y=MEDIAN_MASS, color=TEMPERATURE)) +
geom_point(alpha=0.05) +
stat_smooth(method = "lm") +
ylim(0,0.15) +
theme_classic()
plot2 <- ggplot(m1_df, aes(x=MASS_FEMALE, y=MEDIAN_MASS, color=TEMPERATURE)) +
geom_point(alpha=0.05) +
stat_smooth(method = "lm") +
ylim(0,0.15) +
theme_classic()
plot3 <- ggplot(m1_df, aes(x=MASS_MIDPOINT, y=MEDIAN_MASS, color=TEMPERATURE)) +
geom_point(alpha=0.05) +
stat_smooth(method = "lm") +
ylim(0,0.15) +
theme_classic()
ggarrange(plot1, plot2, plot3,
nrow =1,
ncol =3,
common.legend = TRUE)| POPULATION | 27 | 28.5 | 30 |
|---|---|---|---|
| Arlington Reef | 8 | 8 | 8 |
| Pretty patches | 4 | 6 | 6 |
| Sudbury Reef | 4 | 4 | 2 |
| Vlassof cay | 6 | 2 | 6 |
| POPULATION | 27 | 28.5 | 30 |
|---|---|---|---|
| Arlington Reef | 8 | 4 | 7 |
| Pretty Patches | 4 | 3 | 4 |
| Sudbury Reef | 4 | 2 | 2 |
| Vlassof Cay | 4 | 1 | 4 |
| POPULATION | 27 | 28.5 | 30 |
|---|---|---|---|
| Arlington Reef | 7 | 4 | 6 |
| Pretty Patches | 4 | 3 | 5 |
| Sudbury Reef | 4 | 2 | 1 |
| Vlassof Cay | 3 | 3 | 4 |
| POPULATION | 27 | 28.5 | 30 |
|---|---|---|---|
| Arlington Reef | 8 | 5 | 8 |
| Pretty Patches | 4 | 3 | 4 |
| Sudbury Reef | 3 | 2 | 2 |
| Vlassof Cay | 3 | 2 | 4 |
datasummary(Factor(TEMPERATURE) ~ MASS * (NUnique + mean + median + min + max + sd + Histogram),
data = drop_na(adult, MASS),
fmt = "%.2f")| TEMPERATURE | NUnique | mean | median | min | max | sd | Histogram |
|---|---|---|---|---|---|---|---|
| 27 | 21 | 46.93 | 50.63 | 29.85 | 59.93 | 10.30 | ▇▁▃▄▄▆▄ |
| 28.5 | 20 | 38.81 | 42.36 | 16.28 | 53.26 | 10.26 | ▁▁▄▃▄▇▆▁ |
| 30 | 22 | 39.94 | 39.62 | 23.91 | 57.31 | 9.43 | ▅▇▂▇▇▇▂▇▅▂ |
datasummary(Factor(TEMPERATURE) ~ MEDIAN_MASS * (NUnique + mean + median + min + max + sd + Histogram),
data = drop_na(m1_df, MEDIAN_MASS),
fmt = "%.2f")| TEMPERATURE | NUnique | mean | median | min | max | sd | Histogram |
|---|---|---|---|---|---|---|---|
| 27 | 20 | 0.06 | 0.06 | 0.02 | 0.12 | 0.02 | ▁▂▂▇▅▁▂▁▁ |
| 28.5 | 10 | 0.07 | 0.06 | 0.04 | 0.09 | 0.02 | ▃▃▃▇▇▃▇ |
| 30 | 17 | 0.07 | 0.06 | 0.04 | 0.11 | 0.02 | ▅▂▇▇▇▅▂▅ |
datasummary(Factor(TEMPERATURE) ~ MEDIAN_MASS * (NUnique + mean + median + min + max + sd + Histogram),
data = drop_na(m2_df, MEDIAN_MASS),
fmt = "%.2f")| TEMPERATURE | NUnique | mean | median | min | max | sd | Histogram |
|---|---|---|---|---|---|---|---|
| 27 | 18 | 0.27 | 0.27 | 0.15 | 0.36 | 0.05 | ▁▁▁▄▇▁▆▁▁ |
| 28.5 | 11 | 0.28 | 0.27 | 0.21 | 0.34 | 0.03 | ▂▂▅▇▂▂▂▂▂ |
| 30 | 16 | 0.28 | 0.29 | 0.19 | 0.37 | 0.05 | ▃▂▅▇▇▂▂ |
datasummary(Factor(TEMPERATURE) ~ MEDIAN_MASS * (NUnique + mean + median + min + max + sd + Histogram),
data = drop_na(m2.5_df, MEDIAN_MASS),
fmt = "%.2f")| TEMPERATURE | NUnique | mean | median | min | max | sd | Histogram |
|---|---|---|---|---|---|---|---|
| 27 | 18 | 0.48 | 0.47 | 0.27 | 0.70 | 0.10 | ▂▃▅▅▇▅▂▂ |
| 28.5 | 12 | 0.47 | 0.43 | 0.33 | 0.77 | 0.15 | ▇▅▅▅▂▅ |
| 30 | 18 | 0.45 | 0.44 | 0.37 | 0.55 | 0.05 | ▅▂▂▇▅▂▃▃▂ |
modelNULL <- glmmTMB(MEDIAN_MASS ~ 1,
family=gaussian(),
data =m1_df)
model2 <- glmmTMB(MEDIAN_MASS ~ (1|LEVEL),
family=gaussian(),
data = m1_df)
model3 <- glmmTMB(MEDIAN_MASS ~ (1|CLUTCH_ORDER),
family=gaussian(),
data = m1_df)
model4 <- glmmTMB(MEDIAN_MASS ~ (1|REGION),
family=gaussian(),
data = m1_df)
model5 <- glmmTMB(MEDIAN_MASS ~ (1|REGION) + (1|POPULATION),
family=gaussian(),
data = m1_df) ## Warning in finalizeTMB(TMBStruc, obj, fit, h, data.tmb.old): Model convergence
## problem; non-positive-definite Hessian matrix. See vignette('troubleshooting')
model6 <- glmmTMB(MEDIAN_MASS ~ (1|CLUTCH_ORDER) + (1|REGION) + (1|POPULATION),
family=gaussian(),
data = m1_df)
AIC(modelNULL, model2, model3, model4, model5, model6) modelNULL <- glmmTMB(MEDIAN_MASS ~ 1,
family=gaussian(),
data =m2_df)
model2 <- glmmTMB(MEDIAN_MASS ~ (1|LEVEL),
family=gaussian(),
data = m2_df)
model3 <- glmmTMB(MEDIAN_MASS ~ (1|CLUTCH_ORDER),
family=gaussian(),
data = m2_df)
model4 <- glmmTMB(MEDIAN_MASS ~ (1|REGION),
family=gaussian(),
data = m2_df)
model5 <- glmmTMB(MEDIAN_MASS ~ (1|REGION) + (1|POPULATION),
family=gaussian(),
data = m2_df)
model6 <- glmmTMB(MEDIAN_MASS ~ (1|CLUTCH_ORDER) + (1|REGION) + (1|POPULATION),
family=gaussian(),
data = m2_df)
AIC(modelNULL, model2, model3, model4, model5, model6) modelNULL <- glmmTMB(MEDIAN_MASS ~ 1,
family=gaussian(),
data =m2.5_df)
model2 <- glmmTMB(MEDIAN_MASS ~ (1|LEVEL),
family=gaussian(),
data = m2.5_df)
model3 <- glmmTMB(MEDIAN_MASS ~ (1|CLUTCH_ORDER),
family=gaussian(),
data = m2.5_df)
model4 <- glmmTMB(MEDIAN_MASS ~ (1|REGION),
family=gaussian(),
data = m2.5_df)
model5 <- glmmTMB(MEDIAN_MASS ~ (1|REGION) + (1|POPULATION),
family=gaussian(),
data = m2.5_df) ## Warning in finalizeTMB(TMBStruc, obj, fit, h, data.tmb.old): Model convergence
## problem; non-positive-definite Hessian matrix. See vignette('troubleshooting')
model6 <- glmmTMB(MEDIAN_MASS ~ (1|CLUTCH_ORDER) + (1|REGION) + (1|POPULATION),
family=gaussian(),
data = m2.5_df)
AIC(modelNULL, model2, model3, model4, model5, model6) For mass measurements at different time periods, including 1, 2, and 2.5 months the best model is the most simply model (i.e., model1), where the only random factor that is present is CLUTCH_NUMBER.
Now that we have figured out which random factors will be included within out generalized linear mixed effects model we can start to explore different hypothesese by adding in our fixed factors - covariates.
Fixed factors that will be included will be those that are essential to answering the initial research question based on heiritability of traits between offspring and parental fish - labelled as MALE and FEMALE in the dataframe as well as their combined score MIDPOINT, if applicable. TEMPERATURE is also essential to answering the main research question that looks to see if heritability changes at different temperatures.
Our main research hypothesis will be modelled using the formula below”
An alternative research hypothesis will will test will include an interaction with PARENTAL_DAYS_IN_TEMPERATURE to see if heritability was affect by how long adults spent at experimental temperatures. This model may look something like:
Lets start fitting models:
Model1a was selected as the best model and will be used going forward.
## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help.
##
## Scaled residual values: 0.5 0.264 0.856 0.284 0.232 0.952 0.876 0.096 0.144 0.888 1 0.06 0.436 0.072 0.904 0.296 0.196 0.504 0.552 0.424 ...
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.12213, p-value = 0.4849
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0221, p-value = 0.872
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 1, observations = 47, p-value = 0.3134
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.0005385317 0.1129377171
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0.0212766
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.12213, p-value = 0.4849
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0221, p-value = 0.872
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 1, observations = 47, p-value = 0.3134
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.0005385317 0.1129377171
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0.0212766
## `check_outliers()` does not yet support models of class `glmmTMB`.
## NOTE: Results may be misleading due to involvement in interactions
## Family: gaussian ( identity )
## Formula: MEDIAN_MASS ~ scale(MASS_MALE) * TEMPERATURE + scale(DENSITY)
## Data: m1_df
##
## AIC BIC logLik deviance df.resid
## -221.8 -207.0 118.9 -237.8 39
##
##
## Dispersion estimate for gaussian family (sigma^2): 0.000372
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.0578168 0.0048851 11.835 <2e-16 ***
## scale(MASS_MALE) 0.0058811 0.0051837 1.135 0.2566
## TEMPERATURE28.5 0.0088536 0.0081615 1.085 0.2780
## TEMPERATURE30 0.0125701 0.0070335 1.787 0.0739 .
## scale(DENSITY) 0.0001506 0.0031777 0.047 0.9622
## scale(MASS_MALE):TEMPERATURE28.5 -0.0042435 0.0089813 -0.472 0.6366
## scale(MASS_MALE):TEMPERATURE30 -0.0034793 0.0070392 -0.494 0.6211
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 2.5 % 97.5 % Estimate
## (Intercept) 0.048242264 0.067391341 0.0578168021
## scale(MASS_MALE) -0.004278816 0.016041083 0.0058811338
## TEMPERATURE28.5 -0.007142549 0.024849787 0.0088536190
## TEMPERATURE30 -0.001215362 0.026355474 0.0125700562
## scale(DENSITY) -0.006077575 0.006378709 0.0001505672
## scale(MASS_MALE):TEMPERATURE28.5 -0.021846483 0.013359409 -0.0042435370
## scale(MASS_MALE):TEMPERATURE30 -0.017275889 0.010317287 -0.0034793010
## Random effect variances not available. Returned R2 does not account for random effects.
## # R2 for Mixed Models
##
## Conditional R2: NA
## Marginal R2: 0.081
m1.mass <- emmeans(model1a, ~ MASS_MALE*TEMPERATURE,
at =list(MASS_MALE=seq(from =min(m1_df$MASS_MALE), to =max(m1_df$MASS_MALE), by=.25)))
m1.mass.df <- as.data.frame(m1.mass)
m1.mass.obs <- drop_na(m1_df, MASS_MALE, MEDIAN_MASS) |>
mutate(Pred =predict(model1a, re.form=NA, type ='response'),
Resid =residuals(model1a, type ='response'),
Fit =Pred+Resid)
m1.mass.obs.summarize <- m1.mass.obs |>
group_by(CLUTCH_NUMBER, TEMPERATURE) |>
summarise(mean.mass =mean(Fit, na.rm=TRUE),
mean.mass.male =mean(MASS_MALE, na.rm = TRUE),
sd.mass =sd(Fit, na.rm =TRUE),
n.mass = n()) |>
mutate(se.mass = sd.mass / sqrt(n.mass),
lower.ci.mass =mean.mass - qt(1-(0.05/2), n.mass -1) * se.mass,
upper.ci.mass =mean.mass + qt(1-(0.05/2), n.mass -1) * se.mass) |>
ungroup()## `summarise()` has grouped output by 'CLUTCH_NUMBER'. You can override using the
## `.groups` argument.
## Warning: There were 94 warnings in `mutate()`.
## The first warning was:
## ℹ In argument: `lower.ci.mass = mean.mass - qt(1 - (0.05/2), n.mass - 1) *
## se.mass`.
## ℹ In group 1: `CLUTCH_NUMBER = 38`.
## Caused by warning in `qt()`:
## ! NaNs produced
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 93 remaining warnings.
ggplot(data = m1.mass.df, aes(x=MASS_MALE, y=emmean)) +
stat_smooth(aes(color=TEMPERATURE),
method = "lm") +
geom_pointrange(data = m1.mass.obs.summarize, aes(x =mean.mass.male,
y =mean.mass,
ymin =lower.ci.mass,
ymax =upper.ci.mass,
color = TEMPERATURE)) +
scale_color_manual(values = c("#69d7d8","#ff9c56", "#903146")) +
scale_fill_manual(values =c("#69d7d8","#ff9c56", "#903146")) +
facet_wrap(~TEMPERATURE)+
xlab("PARENTAL MALE MASS (g)") +
ylab("OFFSPRING MASS (g)") +
ggtitle("Offspring-male relationship") +
theme_classic()## `geom_smooth()` using formula = 'y ~ x'
## Warning: Removed 20 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 10 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 17 rows containing missing values or values outside the scale range
## (`geom_segment()`).
The null model appears better than the models that we used. Let’s explore the data bit more and see if we can find a reason for this. Let’s start by looking at a basic histogram of our data.
There appears to be a left skew within our data. Let’s see if this can be better modelled with a Gamma distribution. If not we can try to incorporate transformations to our response variable. The model validations below also could use some improving.
## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help.
##
## Scaled residual values: 0.452 0 0.204 0.876 0.564 0.788 0.128 0.824 0.616 0.748 0.96 0.836 0.96 0.856 0.636 0.956 0.32 0.432 0.668 0.472 ...
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.080348, p-value = 0.9278
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0232, p-value = 0.856
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 1, observations = 46, p-value = 0.3079
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.0005502357 0.1152718256
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0.02173913
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.080348, p-value = 0.9278
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0232, p-value = 0.856
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 1, observations = 46, p-value = 0.3079
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.0005502357 0.1152718256
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0.02173913
## `check_outliers()` does not yet support models of class `glmmTMB`.
## NOTE: Results may be misleading due to involvement in interactions
## Family: gaussian ( identity )
## Formula: MEDIAN_MASS ~ scale(MASS_MALE) * TEMPERATURE + scale(DENSITY)
## Data: m2_df
##
## AIC BIC logLik deviance df.resid
## -148.4 -133.7 82.2 -164.4 38
##
##
## Dispersion estimate for gaussian family (sigma^2): 0.00164
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.270381 0.011673 23.162 <2e-16 ***
## scale(MASS_MALE) -0.002550 0.011895 -0.214 0.8303
## TEMPERATURE28.5 0.010136 0.018309 0.554 0.5799
## TEMPERATURE30 0.005808 0.015780 0.368 0.7128
## scale(DENSITY) -0.015049 0.007144 -2.107 0.0352 *
## scale(MASS_MALE):TEMPERATURE28.5 -0.003736 0.019757 -0.189 0.8500
## scale(MASS_MALE):TEMPERATURE30 0.004556 0.014829 0.307 0.7587
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 2.5 % 97.5 % Estimate
## (Intercept) 0.24750182 0.293260769 0.270381294
## scale(MASS_MALE) -0.02586306 0.020763890 -0.002549585
## TEMPERATURE28.5 -0.02574975 0.046021385 0.010135819
## TEMPERATURE30 -0.02512076 0.036737207 0.005808224
## scale(DENSITY) -0.02905035 -0.001047521 -0.015048934
## scale(MASS_MALE):TEMPERATURE28.5 -0.04245986 0.034987351 -0.003736256
## scale(MASS_MALE):TEMPERATURE30 -0.02450841 0.033619677 0.004555633
## Random effect variances not available. Returned R2 does not account for random effects.
## # R2 for Mixed Models
##
## Conditional R2: NA
## Marginal R2: 0.124
m2.mass <- emmeans(model1a, ~ MASS_MALE*TEMPERATURE,
at =list(MASS_MALE=seq(from =min(m2_df$MASS_MALE), to =max(m2_df$MASS_MALE), by=.25)))
m2.mass.df <- as.data.frame(m2.mass)
m2.mass.obs <- drop_na(m2_df, MASS_MALE, MEDIAN_MASS) |>
mutate(Pred =predict(model1a, re.form=NA, type ='response'),
Resid =residuals(model1a, type ='response'),
Fit =Pred+Resid)
m2.mass.obs.summarize <- m2.mass.obs |>
group_by(CLUTCH_NUMBER, TEMPERATURE) |>
summarise(mean.mass =mean(Fit, na.rm=TRUE),
mean.mass.male =mean(MASS_MALE, na.rm = TRUE),
sd.mass =sd(Fit, na.rm =TRUE),
n.mass = n()) |>
mutate(se.mass = sd.mass / sqrt(n.mass),
lower.ci.mass =mean.mass - qt(1-(0.05/2), n.mass -1) * se.mass,
upper.ci.mass =mean.mass + qt(1-(0.05/2), n.mass -1) * se.mass) |>
ungroup()## `summarise()` has grouped output by 'CLUTCH_NUMBER'. You can override using the
## `.groups` argument.
## Warning: There were 88 warnings in `mutate()`.
## The first warning was:
## ℹ In argument: `lower.ci.mass = mean.mass - qt(1 - (0.05/2), n.mass - 1) *
## se.mass`.
## ℹ In group 1: `CLUTCH_NUMBER = 38`.
## Caused by warning in `qt()`:
## ! NaNs produced
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 87 remaining warnings.
ggplot(data = m2.mass.df, aes(x=MASS_MALE, y=emmean)) +
stat_smooth(aes(color=TEMPERATURE),
method = "lm",
formula = y ~ x) +
geom_pointrange(data = m2.mass.obs.summarize, aes(x =mean.mass.male,
y =mean.mass,
ymin =lower.ci.mass,
ymax =upper.ci.mass,
color = TEMPERATURE)) +
scale_color_manual(values = c("#69d7d8","#ff9c56", "#903146")) +
scale_fill_manual(values =c("#69d7d8","#ff9c56", "#903146")) +
facet_wrap(~TEMPERATURE)+
xlab("PARENTAL MALE STANDARD LENGTH (mm)") +
ylab("OFFSPRING STANDARD LENGTH (mm)") +
ggtitle("Offspring-male relationship") +
theme_classic()## Warning: Removed 18 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 10 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 16 rows containing missing values or values outside the scale range
## (`geom_segment()`).
Once again the NULL model seems to outperform our hypothesis testing models. Let’s follow the steps that we conducted for 2-month data and appy a log transformation to our dataset to see if it improved the model.
## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help.
##
## Scaled residual values: 0.988 0.744 0.792 0.156 0.596 0.956 0.776 0.844 0.896 0.568 0.768 0.944 0.68 0.46 0.3 0.952 0.768 0.724 0.42 0.804 ...
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.078833, p-value = 0.9266
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0217, p-value = 0.88
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 0, observations = 48, p-value = 1
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.00000000 0.07397279
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.078833, p-value = 0.9266
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0217, p-value = 0.88
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 0, observations = 48, p-value = 1
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.00000000 0.07397279
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0
## `check_outliers()` does not yet support models of class `glmmTMB`.
## NOTE: Results may be misleading due to involvement in interactions
## Family: gaussian ( identity )
## Formula: MEDIAN_MASS ~ scale(MASS_MALE) * TEMPERATURE + scale(DENSITY)
## Data: m2.5_df
##
## AIC BIC logLik deviance df.resid
## -109.0 -94.0 62.5 -125.0 40
##
##
## Dispersion estimate for gaussian family (sigma^2): 0.00433
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.471464 0.017449 27.020 < 2e-16 ***
## scale(MASS_MALE) 0.025374 0.016358 1.551 0.121
## TEMPERATURE28.5 -0.020863 0.026902 -0.776 0.438
## TEMPERATURE30 -0.014006 0.023848 -0.587 0.557
## scale(DENSITY) -0.072959 0.009758 -7.477 7.63e-14 ***
## scale(MASS_MALE):TEMPERATURE28.5 -0.045901 0.030630 -1.499 0.134
## scale(MASS_MALE):TEMPERATURE30 -0.013601 0.022733 -0.598 0.550
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 2.5 % 97.5 % Estimate
## (Intercept) 0.43726427 0.50566312 0.47146369
## scale(MASS_MALE) -0.00668662 0.05743449 0.02537393
## TEMPERATURE28.5 -0.07359025 0.03186350 -0.02086337
## TEMPERATURE30 -0.06074605 0.03273487 -0.01400559
## scale(DENSITY) -0.09208455 -0.05383293 -0.07295874
## scale(MASS_MALE):TEMPERATURE28.5 -0.10593556 0.01413293 -0.04590131
## scale(MASS_MALE):TEMPERATURE30 -0.05815793 0.03095547 -0.01360123
## Random effect variances not available. Returned R2 does not account for random effects.
## # R2 for Mixed Models
##
## Conditional R2: NA
## Marginal R2: 0.561
m1.mass <- emmeans(model1a, ~ MASS_MALE*TEMPERATURE,
at =list(MASS_MALE=seq(from =min(m2.5_df$MASS_MALE), to =max(m2.5_df$MASS_MALE), by=.25)))
m1.mass.df <- as.data.frame(m1.mass)
m1.mass.obs <- drop_na(m2.5_df, MASS_MALE, MEDIAN_MASS) |>
mutate(Pred =predict(model1a, re.form=NA, type ='response'),
Resid =residuals(model1a, type ='response'),
Fit =Pred+Resid)
m1.mass.obs.summarize <- m1.mass.obs |>
group_by(CLUTCH_NUMBER, TEMPERATURE) |>
summarise(mean.mass =mean(Fit, na.rm=TRUE),
mean.mass.male =mean(MASS_MALE, na.rm = TRUE),
sd.mass =sd(Fit, na.rm =TRUE),
n.mass = n()) |>
mutate(se.mass = sd.mass / sqrt(n.mass),
lower.ci.mass =mean.mass - qt(1-(0.05/2), n.mass -1) * se.mass,
upper.ci.mass =mean.mass + qt(1-(0.05/2), n.mass -1) * se.mass) |>
ungroup()## `summarise()` has grouped output by 'CLUTCH_NUMBER'. You can override using the
## `.groups` argument.
## Warning: There were 96 warnings in `mutate()`.
## The first warning was:
## ℹ In argument: `lower.ci.mass = mean.mass - qt(1 - (0.05/2), n.mass - 1) *
## se.mass`.
## ℹ In group 1: `CLUTCH_NUMBER = 38`.
## Caused by warning in `qt()`:
## ! NaNs produced
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 95 remaining warnings.
ggplot(data = m1.mass.df, aes(x=MASS_MALE, y=emmean)) +
stat_smooth(aes(color=TEMPERATURE),
method = "lm",
formula = y ~ x) +
geom_pointrange(data = m1.mass.obs.summarize, aes(x =mean.mass.male,
y =mean.mass,
ymin =lower.ci.mass,
ymax =upper.ci.mass,
color = TEMPERATURE)) +
scale_color_manual(values = c("#69d7d8","#ff9c56", "#903146")) +
scale_fill_manual(values =c("#69d7d8","#ff9c56", "#903146")) +
facet_wrap(~TEMPERATURE)+
xlab("PARENTAL MALE MASS (g)") +
ylab("MEDIAN MASS (g)") +
ggtitle("Offspring-male relationship") +
theme_classic()## Warning: Removed 18 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 12 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 18 rows containing missing values or values outside the scale range
## (`geom_segment()`).
Model1a was selected as the best model and will be used going forward.
## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help.
##
## Scaled residual values: 0.504 0.284 0.864 0.264 0.228 0.952 0.852 0.1 0.184 0.884 1 0.052 0.416 0.084 0.912 0.3 0.2 0.496 0.528 0.456 ...
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.12213, p-value = 0.4849
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0221, p-value = 0.872
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 1, observations = 47, p-value = 0.3134
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.0005385317 0.1129377171
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0.0212766
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.12213, p-value = 0.4849
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0221, p-value = 0.872
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 1, observations = 47, p-value = 0.3134
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.0005385317 0.1129377171
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0.0212766
## `check_outliers()` does not yet support models of class `glmmTMB`.
## NOTE: Results may be misleading due to involvement in interactions
## Family: gaussian ( identity )
## Formula:
## MEDIAN_MASS ~ scale(MASS_MIDPOINT) * TEMPERATURE + scale(DENSITY)
## Data: m1_df
##
## AIC BIC logLik deviance df.resid
## -221.6 -206.8 118.8 -237.6 39
##
##
## Dispersion estimate for gaussian family (sigma^2): 0.000373
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.0587013 0.0046690 12.573 <2e-16 ***
## scale(MASS_MIDPOINT) 0.0045869 0.0047451 0.967 0.3337
## TEMPERATURE28.5 0.0086531 0.0080186 1.079 0.2805
## TEMPERATURE30 0.0115693 0.0068154 1.698 0.0896 .
## scale(DENSITY) 0.0001254 0.0031975 0.039 0.9687
## scale(MASS_MIDPOINT):TEMPERATURE28.5 -0.0012688 0.0077652 -0.163 0.8702
## scale(MASS_MIDPOINT):TEMPERATURE30 -0.0015550 0.0071932 -0.216 0.8288
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 2.5 % 97.5 % Estimate
## (Intercept) 0.049550342 0.06785235 0.0587013451
## scale(MASS_MIDPOINT) -0.004713292 0.01388702 0.0045868646
## TEMPERATURE28.5 -0.007063129 0.02436923 0.0086530523
## TEMPERATURE30 -0.001788599 0.02492720 0.0115692983
## scale(DENSITY) -0.006141489 0.00639231 0.0001254108
## scale(MASS_MIDPOINT):TEMPERATURE28.5 -0.016488358 0.01395083 -0.0012687619
## scale(MASS_MIDPOINT):TEMPERATURE30 -0.015653450 0.01254343 -0.0015550098
## Random effect variances not available. Returned R2 does not account for random effects.
## # R2 for Mixed Models
##
## Conditional R2: NA
## Marginal R2: 0.078
m1_df <-
m1_df |>
drop_na(MASS_MIDPOINT)
m1.mass <- emmeans(model1a, ~ MASS_MIDPOINT*TEMPERATURE,
at =list(MASS_MIDPOINT=seq(from =min(m1_df$MASS_MIDPOINT), to =max(m1_df$MASS_MIDPOINT), by=.25)))
m1.mass.df <- as.data.frame(m1.mass)
m1.mass.obs <- drop_na(m1_df, MASS_MIDPOINT, MEDIAN_MASS) |>
mutate(Pred =predict(model1a, re.form=NA, type ='response'),
Resid =residuals(model1a, type ='response'),
Fit =Pred+Resid)
m1.mass.obs.summarize <- m1.mass.obs |>
group_by(CLUTCH_NUMBER, TEMPERATURE) |>
summarise(mean.mass =mean(Fit, na.rm=TRUE),
mean.mass.female =mean(MASS_MIDPOINT, na.rm = TRUE),
sd.mass =sd(Fit, na.rm =TRUE),
n.mass = n()) |>
mutate(se.mass = sd.mass / sqrt(n.mass),
lower.ci.mass =mean.mass - qt(1-(0.05/2), n.mass -1) * se.mass,
upper.ci.mass =mean.mass + qt(1-(0.05/2), n.mass -1) * se.mass) |>
ungroup()## `summarise()` has grouped output by 'CLUTCH_NUMBER'. You can override using the
## `.groups` argument.
## Warning: There were 94 warnings in `mutate()`.
## The first warning was:
## ℹ In argument: `lower.ci.mass = mean.mass - qt(1 - (0.05/2), n.mass - 1) *
## se.mass`.
## ℹ In group 1: `CLUTCH_NUMBER = 38`.
## Caused by warning in `qt()`:
## ! NaNs produced
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 93 remaining warnings.
ggplot(data = m1.mass.df, aes(x=MASS_MIDPOINT, y=emmean)) +
stat_smooth(aes(color=TEMPERATURE),
method = "lm") +
geom_pointrange(data = m1.mass.obs.summarize, aes(x =mean.mass.female,
y =mean.mass,
ymin =lower.ci.mass,
ymax =upper.ci.mass,
color = TEMPERATURE)) +
scale_color_manual(values = c("#69d7d8","#ff9c56", "#903146")) +
scale_fill_manual(values =c("#69d7d8","#ff9c56", "#903146")) +
facet_wrap(~TEMPERATURE)+
xlab("PARENTAL MIDPOINT STANDARD LENGTH (mm)") +
ylab("OFFSPRING STANDARD LENGTH (mm)") +
ggtitle("Offspring-male relationship") +
theme_classic()## `geom_smooth()` using formula = 'y ~ x'
## Warning: Removed 20 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 10 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 17 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning in newton(lsp = lsp, X = G$X, y = G$y, Eb = G$Eb, UrS = G$UrS, L = G$L,
## : Fitting terminated with step failure - check results carefully
## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help.
##
## Scaled residual values: 0.452 0 0.224 0.884 0.568 0.78 0.128 0.892 0.668 0.784 0.96 0.808 0.936 0.856 0.656 0.952 0.32 0.428 0.664 0.604 ...
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.089391, p-value = 0.8559
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0232, p-value = 0.856
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 1, observations = 46, p-value = 0.3079
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.0005502357 0.1152718256
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0.02173913
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.089391, p-value = 0.8559
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0232, p-value = 0.856
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 1, observations = 46, p-value = 0.3079
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.0005502357 0.1152718256
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0.02173913
## `check_outliers()` does not yet support models of class `glmmTMB`.
## Warning in newton(lsp = lsp, X = G$X, y = G$y, Eb = G$Eb, UrS = G$UrS, L = G$L,
## : Fitting terminated with step failure - check results carefully
## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help.
##
## Scaled residual values: 0.452 0 0.224 0.884 0.568 0.78 0.128 0.892 0.668 0.784 0.96 0.808 0.936 0.856 0.656 0.952 0.32 0.428 0.664 0.604 ...
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.089391, p-value = 0.8559
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0232, p-value = 0.856
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 1, observations = 46, p-value = 0.3079
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.0005502357 0.1152718256
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0.02173913
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.089391, p-value = 0.8559
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0232, p-value = 0.856
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 1, observations = 46, p-value = 0.3079
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.0005502357 0.1152718256
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0.02173913
## `check_outliers()` does not yet support models of class `glmmTMB`.
## NOTE: Results may be misleading due to involvement in interactions
## Family: gaussian ( identity )
## Formula:
## MEDIAN_MASS ~ scale(MASS_MIDPOINT) * TEMPERATURE + scale(DENSITY)
## Data: m2_df
##
## AIC BIC logLik deviance df.resid
## -148.5 -133.9 82.3 -164.5 38
##
##
## Dispersion estimate for gaussian family (sigma^2): 0.00164
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.270698 0.010849 24.951 <2e-16 ***
## scale(MASS_MIDPOINT) -0.002989 0.010562 -0.283 0.7772
## TEMPERATURE28.5 0.010798 0.017496 0.617 0.5371
## TEMPERATURE30 0.003479 0.015047 0.231 0.8172
## scale(DENSITY) -0.013287 0.007221 -1.840 0.0658 .
## scale(MASS_MIDPOINT):TEMPERATURE28.5 0.001755 0.016633 0.105 0.9160
## scale(MASS_MIDPOINT):TEMPERATURE30 -0.004617 0.015067 -0.306 0.7593
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 2.5 % 97.5 % Estimate
## (Intercept) 0.24943399 0.2919622252 0.270698107
## scale(MASS_MIDPOINT) -0.02368984 0.0177121013 -0.002988872
## TEMPERATURE28.5 -0.02349337 0.0450889225 0.010797777
## TEMPERATURE30 -0.02601319 0.0329705215 0.003478665
## scale(DENSITY) -0.02743873 0.0008655102 -0.013286607
## scale(MASS_MIDPOINT):TEMPERATURE28.5 -0.03084546 0.0343545490 0.001754542
## scale(MASS_MIDPOINT):TEMPERATURE30 -0.03414709 0.0249129745 -0.004617056
## Random effect variances not available. Returned R2 does not account for random effects.
## # R2 for Mixed Models
##
## Conditional R2: NA
## Marginal R2: 0.127
m2_df <-
m2_df |>
drop_na(MASS_MIDPOINT)
m2.mass <- emmeans(model1a, ~ MASS_MIDPOINT*TEMPERATURE,
at =list(MASS_MIDPOINT=seq(from =min(m2_df$MASS_MIDPOINT), to =max(m2_df$MASS_MIDPOINT), by=.25)))
m2.mass.df <- as.data.frame(m2.mass)
m2.mass.obs <- drop_na(m2_df, MASS_MIDPOINT,MEDIAN_MASS) |>
mutate(Pred =predict(model1a, re.form=NA, type ='response'),
Resid =residuals(model1a, type ='response'),
Fit =Pred+Resid)
m2.mass.obs.summarize <- m2.mass.obs |>
group_by(CLUTCH_NUMBER, TEMPERATURE) |>
summarise(mean.mass =mean(Fit, na.rm=TRUE),
mean.mass.male =mean(MASS_MIDPOINT, na.rm = TRUE),
sd.mass =sd(Fit, na.rm =TRUE),
n.mass = n()) |>
mutate(se.mass = sd.mass / sqrt(n.mass),
lower.ci.mass =mean.mass - qt(1-(0.05/2), n.mass -1) * se.mass,
upper.ci.mass =mean.mass + qt(1-(0.05/2), n.mass -1) * se.mass) |>
ungroup()## `summarise()` has grouped output by 'CLUTCH_NUMBER'. You can override using the
## `.groups` argument.
## Warning: There were 88 warnings in `mutate()`.
## The first warning was:
## ℹ In argument: `lower.ci.mass = mean.mass - qt(1 - (0.05/2), n.mass - 1) *
## se.mass`.
## ℹ In group 1: `CLUTCH_NUMBER = 38`.
## Caused by warning in `qt()`:
## ! NaNs produced
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 87 remaining warnings.
ggplot(data = m2.mass.df, aes(x=MASS_MIDPOINT, y=emmean)) +
stat_smooth(aes(color=TEMPERATURE),
method = "lm",
formula = y ~ x) +
geom_pointrange(data = m2.mass.obs.summarize, aes(x =mean.mass.male,
y =mean.mass,
ymin =lower.ci.mass,
ymax =upper.ci.mass,
color = TEMPERATURE)) +
scale_color_manual(values = c("#69d7d8","#ff9c56", "#903146")) +
scale_fill_manual(values =c("#69d7d8","#ff9c56", "#903146")) +
facet_wrap(~TEMPERATURE)+
xlab("PARENTAL MIDPOINT STANDARD LENGTH (mm)") +
ylab("OFFSPRING STANDARD LENGTH (mm)") +
ggtitle("Offspring-male relationship") +
theme_classic()## Warning: Removed 18 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 10 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 16 rows containing missing values or values outside the scale range
## (`geom_segment()`).
Once again the NULL model seems to outperform our hypothesis testing models. Let’s follow the steps that we conducted for 2-month data and appy a log transformation to our dataset to see if it improved the model.
## Object of Class DHARMa with simulated residuals based on 250 simulations with refit = FALSE . See ?DHARMa::simulateResiduals for help.
##
## Scaled residual values: 0.992 0.748 0.768 0.12 0.644 0.964 0.752 0.88 0.9 0.556 0.76 0.936 0.644 0.508 0.308 0.952 0.72 0.748 0.4 0.784 ...
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.070167, p-value = 0.9721
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0217, p-value = 0.88
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 0, observations = 48, p-value = 1
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.00000000 0.07397279
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0
## $uniformity
##
## Asymptotic one-sample Kolmogorov-Smirnov test
##
## data: simulationOutput$scaledResiduals
## D = 0.070167, p-value = 0.9721
## alternative hypothesis: two-sided
##
##
## $dispersion
##
## DHARMa nonparametric dispersion test via sd of residuals fitted vs.
## simulated
##
## data: simulationOutput
## dispersion = 1.0217, p-value = 0.88
## alternative hypothesis: two.sided
##
##
## $outliers
##
## DHARMa outlier test based on exact binomial test with approximate
## expectations
##
## data: simulationOutput
## outliers at both margin(s) = 0, observations = 48, p-value = 1
## alternative hypothesis: true probability of success is not equal to 0.007968127
## 95 percent confidence interval:
## 0.00000000 0.07397279
## sample estimates:
## frequency of outliers (expected: 0.00796812749003984 )
## 0
## `check_outliers()` does not yet support models of class `glmmTMB`.
## NOTE: Results may be misleading due to involvement in interactions
## Family: gaussian ( identity )
## Formula:
## MEDIAN_MASS ~ scale(MASS_MIDPOINT) * TEMPERATURE + scale(DENSITY)
## Data: m2.5_df
##
## AIC BIC logLik deviance df.resid
## -108.2 -93.3 62.1 -124.2 40
##
##
## Dispersion estimate for gaussian family (sigma^2): 0.0044
##
## Conditional model:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.474818 0.016758 28.334 < 2e-16 ***
## scale(MASS_MIDPOINT) 0.022410 0.015057 1.488 0.137
## TEMPERATURE28.5 -0.022567 0.026313 -0.858 0.391
## TEMPERATURE30 -0.019369 0.023234 -0.834 0.404
## scale(DENSITY) -0.072548 0.009812 -7.394 1.42e-13 ***
## scale(MASS_MIDPOINT):TEMPERATURE28.5 -0.036351 0.026549 -1.369 0.171
## scale(MASS_MIDPOINT):TEMPERATURE30 -0.014608 0.023392 -0.624 0.532
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 2.5 % 97.5 % Estimate
## (Intercept) 0.441972967 0.50766224 0.47481760
## scale(MASS_MIDPOINT) -0.007100349 0.05192105 0.02241035
## TEMPERATURE28.5 -0.074138950 0.02900582 -0.02256656
## TEMPERATURE30 -0.064906106 0.02616898 -0.01936856
## scale(DENSITY) -0.091778279 -0.05331715 -0.07254771
## scale(MASS_MIDPOINT):TEMPERATURE28.5 -0.088386829 0.01568507 -0.03635088
## scale(MASS_MIDPOINT):TEMPERATURE30 -0.060454561 0.03123867 -0.01460795
## Random effect variances not available. Returned R2 does not account for random effects.
## # R2 for Mixed Models
##
## Conditional R2: NA
## Marginal R2: 0.555
m2.5_df <- m2.5_df |>
drop_na(MASS_MIDPOINT)
m2.5.mass <- emmeans(model1a, ~ MASS_MIDPOINT*TEMPERATURE,
at =list(MASS_MIDPOINT=seq(from =min(m2.5_df$MASS_MIDPOINT), to =max(m2.5_df$MASS_MIDPOINT), by=.25)))
m2.5.mass.df <- as.data.frame(m2.5.mass)
m2.5.mass.obs <- drop_na(m2.5_df, MASS_MIDPOINT, MEDIAN_MASS) |>
mutate(Pred =predict(model1a, re.form=NA, type ='response'),
Resid =residuals(model1a, type ='response'),
Fit =Pred+Resid)
m2.5.mass.obs.summarize <- m2.5.mass.obs |>
group_by(CLUTCH_NUMBER, TEMPERATURE) |>
summarise(mean.mass =mean(Fit, na.rm=TRUE),
mean.mass.male =mean(MASS_MIDPOINT, na.rm = TRUE),
sd.mass =sd(Fit, na.rm =TRUE),
n.mass = n()) |>
mutate(se.mass = sd.mass / sqrt(n.mass),
lower.ci.mass =mean.mass - qt(1-(0.05/2), n.mass -1) * se.mass,
upper.ci.mass =mean.mass + qt(1-(0.05/2), n.mass -1) * se.mass) |>
ungroup()## `summarise()` has grouped output by 'CLUTCH_NUMBER'. You can override using the
## `.groups` argument.
## Warning: There were 96 warnings in `mutate()`.
## The first warning was:
## ℹ In argument: `lower.ci.mass = mean.mass - qt(1 - (0.05/2), n.mass - 1) *
## se.mass`.
## ℹ In group 1: `CLUTCH_NUMBER = 38`.
## Caused by warning in `qt()`:
## ! NaNs produced
## ℹ Run `dplyr::last_dplyr_warnings()` to see the 95 remaining warnings.
ggplot(data = m2.5.mass.df, aes(x=MASS_MIDPOINT, y=emmean)) +
stat_smooth(aes(color=TEMPERATURE),
method = "lm",
formula = y ~ x) +
geom_pointrange(data = m2.5.mass.obs.summarize, aes(x =mean.mass.male,
y =mean.mass,
ymin =lower.ci.mass,
ymax =upper.ci.mass,
color = TEMPERATURE)) +
scale_color_manual(values = c("#69d7d8","#ff9c56", "#903146")) +
scale_fill_manual(values =c("#69d7d8","#ff9c56", "#903146")) +
facet_wrap(~TEMPERATURE)+
xlab("PARENTAL MALE STANDARD LENGTH (mm)") +
ylab("OFFSPRING STANDARD LENGTH (mm)") +
ggtitle("Offspring-male relationship") +
theme_classic()## Warning: Removed 18 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 12 rows containing missing values or values outside the scale range
## (`geom_segment()`).
## Warning: Removed 18 rows containing missing values or values outside the scale range
## (`geom_segment()`).